A Textbook of Data Structures and Algorithms, Volume 1: Mastering Linear Data Structures

284 Pages·2023·8.274 MB·English

by  G. A. Vijayalakshmi Pai

A Textbook of Data Structures and Algorithms 1
One of the greatest lessons I have learnt in my life is
to pay as much attention to the means of work as to its end…
I have been always learning great lessons from that one principle,
and it appears to me that all the secret of success is there;
to pay as much attention to the means as to the end….
Let us perfect the means; the end will take care of itself.

– Swami Vivekananda
(Lecture Delivered at Los Angeles, California, January 4, 1900)
A Textbook of Data
Structures and Algorithms 1

Mastering Linear Data Structures

G A Vijayalakshmi Pai
First published 2022 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.
Previous edition published in 2008 as “Data Structures and Algorithms: Concepts, Techniques and
Applications” by McGraw Hill Education (India) Pvt Ltd. © McGraw Hill Education (India) Pvt Ltd. 2008
Apart from any fair dealing for the purposes of research or private study, or criticism or review, as
permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced,
stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers,
or in the case of reprographic reproduction in accordance with the terms and licenses issued by the
CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the
undermentioned address:
ISTE Ltd John Wiley & Sons, Inc.
27-37 St George’s Road 111 River Street
London SW19 4EU Hoboken, NJ 07030
UK USA
www.iste.co.uk www.wiley.com

© ISTE Ltd 2022
The rights of G A Vijayalakshmi Pai to be identified as the author of this work have been asserted by her
in accordance with the Copyright, Designs and Patents Act 1988.
Any opinions, findings, and conclusions or recommendations expressed in this material are those of the

author(s), contributor(s) or editor(s) and do not necessarily reflect the views of ISTE Group.
Library of Congress Control Number: 2022945771

British Library Cataloguing-in-Publication Data
A CIP record for this book is available from the British Library
ISBN 978-1-78630-869-6
Contents
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv
Chapter 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1. History of algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2. Definition, structure and properties of algorithms . . . . . . . . . . . . . 4
1.2.1. Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2.2. Structure and properties . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3. Development of an algorithm . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.4. Data structures and algorithms . . . . . . . . . . . . . . . . . . . . . . . . 6
1.5. Data structures – definition and classification . . . . . . . . . . . . . . . 7
1.5.1. Abstract data types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.5.2. Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.6. Algorithm design techniques . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.7. Organization of the book . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Chapter 2. Analysis of Algorithms . . . . . . . . . . . . . . . . . . . . . . . 13
2.1. Efficiency of algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2. Apriori analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.3. Asymptotic notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.4. Time complexity of an algorithm using the O notation . . . . . . . . . . 19
2.5. Polynomial time versus exponential time algorithms . . . . . . . . . . . 20
2.6. Average, best and worst case complexities . . . . . . . . . . . . . . . . . 21
vi A Textbook of Data Structures and Algorithms 1
2.7. Analyzing recursive programs . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.7.1. Recursive procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.7.2. Apriori analysis of recursive functions . . . . . . . . . . . . . . . . . 27
2.8. Illustrative problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Chapter 3. Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.2. Array operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.3. Number of elements in an array . . . . . . . . . . . . . . . . . . . . . . . . 46
3.3.1. One-dimensional array . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.3.2. Two-dimensional array . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.3.3. Multidimensional array . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.4. Representation of arrays in memory . . . . . . . . . . . . . . . . . . . . . 48
3.4.1. One-dimensional array . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.4.2. Two-dimensional arrays . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.4.3. Three-dimensional arrays . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.4.4. N-dimensional array . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.5. Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.5.1. Sparse matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.5.2. Ordered lists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.5.3. Strings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.5.4. Bit array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.6. Illustrative problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
Chapter 4. Stacks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.2. Stack operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4.2.1. Stack implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.2.2. Implementation of push and pop operations . . . . . . . . . . . . . . 74
4.3. Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.3.1. Recursive programming . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.3.2. Evaluation of expressions . . . . . . . . . . . . . . . . . . . . . . . . . 79
4.4. Illustrative problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
Chapter 5. Queues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
5.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
5.2. Operations on queues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
5.2.1. Queue implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
5.2.2. Implementation of insert and delete operations on a queue . . . . . 103
Contents vii
5.2.3. Limitations of linear queues. . . . . . . . . . . . . . . . . . . . . . . . 105
5.3. Circular queues. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
5.3.1. Operations on a circular queue . . . . . . . . . . . . . . . . . . . . . . 106
5.3.2. Implementation of insertion and deletion operations in
circular queue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
5.4. Other types of queues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
5.4.1. Priority queues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
5.4.2. Deques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
5.5. Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
5.5.1. Application of a linear queue . . . . . . . . . . . . . . . . . . . . . . . 119
5.5.2. Application of priority queues . . . . . . . . . . . . . . . . . . . . . . 120
5.6. Illustrative problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
Chapter 6. Linked Lists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
6.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
6.1.1. Drawbacks of sequential data structures . . . . . . . . . . . . . . . . 143
6.1.2. Merits of linked data structures . . . . . . . . . . . . . . . . . . . . . . 145
6.1.3. Linked lists – structure and implementation . . . . . . . . . . . . . . 145
6.2. Singly linked lists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
6.2.1. Representation of a singly linked list . . . . . . . . . . . . . . . . . . 147
6.2.2. Insertion and deletion in a singly linked list . . . . . . . . . . . . . . 149
6.3. Circularly linked lists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
6.3.1. Representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
6.3.2. Advantages of circularly linked lists over singly linked lists . . . . 155
6.3.3. Disadvantages of circularly linked lists . . . . . . . . . . . . . . . . . 156
6.3.4. Primitive operations on circularly linked lists . . . . . . . . . . . . . 158
6.3.5. Other operations on circularly linked lists . . . . . . . . . . . . . . . 159
6.4. Doubly linked lists. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
6.4.1. Representation of a doubly linked list . . . . . . . . . . . . . . . . . . 161
6.4.2. Advantages and disadvantages of a doubly linked list . . . . . . . . 162
6.4.3. Operations on doubly linked lists . . . . . . . . . . . . . . . . . . . . 163
6.5. Multiply linked lists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
6.6. Unrolled linked lists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
6.6.1. Retrieval of an element . . . . . . . . . . . . . . . . . . . . . . . . . . 172
6.6.2. Insert an element . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
6.6.3. Delete an element . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
6.7. Self-organizing lists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
6.8. Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
6.8.1. Addition of polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . 176
6.8.2. Sparse matrix representation . . . . . . . . . . . . . . . . . . . . . . . 178
6.9. Illustrative problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
viii A Textbook of Data Structures and Algorithms 1
Chapter 7. Linked Stacks and Linked Queues . . . . . . . . . . . . . . . 201
7.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
7.1.1. Linked stack . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
7.1.2. Linked queues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
7.2. Operations on linked stacks and linked queues . . . . . . . . . . . . . . . 203
7.2.1. Linked stack operations . . . . . . . . . . . . . . . . . . . . . . . . . . 203
7.2.2. Linked queue operations . . . . . . . . . . . . . . . . . . . . . . . . . . 204
7.2.3. Algorithms for Push/Pop operations on a linked stack . . . . . . . . 205
7.2.4. Algorithms for insert and delete operations in a linked queue . . . . 206
7.3. Dynamic memory management and linked stacks . . . . . . . . . . . . . 209
7.4. Implementation of linked representations . . . . . . . . . . . . . . . . . . 214
7.5. Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
7.5.1. Balancing symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
7.5.2. Polynomial representation . . . . . . . . . . . . . . . . . . . . . . . . . 218
7.6. Illustrative problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
Summaries of other volumes . . . . . . . . . . . . . . . . . . . . . . . . . . . 245